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Feature subset weighting for distance-based supervised learning

Adnan Theerens (UGent) , Yvan Saeys (UGent) and Chris Cornelis (UGent)
(2026) PATTERN RECOGNITION. 172(Part A).
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Abstract
This paper introduces feature subset weighting using monotone measures for distance-based supervised learning. The Choquet integral is used to define a distance function that incorporates these weights. This integration enables the proposed distances to effectively capture non-linear relationships and account for interactions both between conditional and decision attributes and among conditional attributes themselves, resulting in a more flexible distance measure. In particular, we show how this approach ensures that the distances remain unaffected by the addition of duplicate and strongly correlated features. Another key point of this approach is that it makes feature subset weighting computationally feasible, since only m feature subset weights should be calculated each time instead of calculating all feature subset weights (2^m), where m is the number of attributes. Next, we also examine how the use of the Choquet integral for measuring similarity leads to a non-equivalent definition of distance. The relationship between distance and similarity is further explored through dual measures. Additionally, symmetric Choquet distances and similarities are proposed, preserving the classical symmetry between similarity and distance. Finally, we introduce a concrete feature subset weighting distance, evaluate its performance in a k-nearest neighbours (KNN) classification setting, and compare it against Mahalanobis distances and weighted distance methods.
Keywords
Distance measures, Choquet integral, Machine learning, Metric learning, K-nearest neighbours, Fuzzy rough sets

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Citation

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MLA
Theerens, Adnan, et al. “Feature Subset Weighting for Distance-Based Supervised Learning.” PATTERN RECOGNITION, vol. 172, no. Part A, 2026, doi:10.1016/j.patcog.2025.112424.
APA
Theerens, A., Saeys, Y., & Cornelis, C. (2026). Feature subset weighting for distance-based supervised learning. PATTERN RECOGNITION, 172(Part A). https://doi.org/10.1016/j.patcog.2025.112424
Chicago author-date
Theerens, Adnan, Yvan Saeys, and Chris Cornelis. 2026. “Feature Subset Weighting for Distance-Based Supervised Learning.” PATTERN RECOGNITION 172 (Part A). https://doi.org/10.1016/j.patcog.2025.112424.
Chicago author-date (all authors)
Theerens, Adnan, Yvan Saeys, and Chris Cornelis. 2026. “Feature Subset Weighting for Distance-Based Supervised Learning.” PATTERN RECOGNITION 172 (Part A). doi:10.1016/j.patcog.2025.112424.
Vancouver
1.
Theerens A, Saeys Y, Cornelis C. Feature subset weighting for distance-based supervised learning. PATTERN RECOGNITION. 2026;172(Part A).
IEEE
[1]
A. Theerens, Y. Saeys, and C. Cornelis, “Feature subset weighting for distance-based supervised learning,” PATTERN RECOGNITION, vol. 172, no. Part A, 2026.
@article{01K524VVT0YQXRWAJB4TYAB760,
  abstract     = {{This paper introduces feature subset weighting using monotone measures for distance-based supervised learning. The Choquet integral is used to define a distance function that incorporates these weights. This integration enables the proposed distances to effectively capture non-linear relationships and account for interactions both between conditional and decision attributes and among conditional attributes themselves, resulting in a more flexible distance measure. In particular, we show how this approach ensures that the distances remain unaffected by the addition of duplicate and strongly correlated features. Another key point of this approach is that it makes feature subset weighting computationally feasible, since only m feature subset weights should be calculated each time instead of calculating all feature subset weights (2^m), where m is the number of attributes. Next, we also examine how the use of the Choquet integral for measuring similarity leads to a non-equivalent definition of distance. The relationship between distance and similarity is further explored through dual measures. Additionally, symmetric Choquet distances and similarities are proposed, preserving the classical symmetry between similarity and distance. Finally, we introduce a concrete feature subset weighting distance, evaluate its performance in a k-nearest neighbours (KNN) classification setting, and compare it against Mahalanobis distances and weighted distance methods.}},
  articleno    = {{112424}},
  author       = {{Theerens, Adnan and Saeys, Yvan and Cornelis, Chris}},
  issn         = {{0031-3203}},
  journal      = {{PATTERN RECOGNITION}},
  keywords     = {{Distance measures,Choquet integral,Machine learning,Metric learning,K-nearest neighbours,Fuzzy rough sets}},
  language     = {{eng}},
  number       = {{Part A}},
  pages        = {{15}},
  title        = {{Feature subset weighting for distance-based supervised learning}},
  url          = {{http://doi.org/10.1016/j.patcog.2025.112424}},
  volume       = {{172}},
  year         = {{2026}},
}
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